I'd ask if you have any bubble corals, but I've found that a reefer's sense of humor is poor when something is going wrong in their tank

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It is not likely that the circulation pumps are causing the bubbles, since I doubt they're powerful enough to cause cavitation; something has to be mixing air with the water. You say the bubbles clear when everything is off, but try turning off just the circulation pumps, one at a time, and see if that makes a difference. I suspect the pumps are just distributing bubbles that are being produced by some other means (skimmer is the most likely. Perhaps the return pump/return line has a hole in it that is drawing in air.)
If you end up finding that one of the circ. pumps are causing the bubbles, it might be that the pump is placed too high in the tank and is drawing air down from the surface. This would be an easy thing to fix.